Fill a large pot with lightly salted water and bring it to a boil
over medium-high heat. Once the water is boiling, stir in the
bow tie pasta and return to a boil. Cook the pasta, uncovered,
until al dente, about 11 minutes. Drain and set aside.
Cook the sausage in a large sauté pan over high heat until cooked
through, about 10 minutes. Add the garlic and sauté for 3
minutes. Add the butter and enough broth to cover the sausage,
bring to a boil over medium-high heat, then add the broccoli and
cook for 5 minutes. Reduce the heat to medium, add the cheeses,
and stir until melted. Place the cooked pasta in a big bowl, add
the sauce mixture, sprinkle with red pepper flakes, and serve.